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Shape Deformation

Shape Deformation

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Shape Deformation

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  1. Shape Deformation Reporter: Zhang, Lei 5/30/2006

  2. Stuff • Vector Field Based Shape Deformation (VFSD) • Multigrid Alogrithm for Deformation • Edit Deforming Surface Animation • Subspace Gradient Domain Mesh Deformation J. Huang, X. H. Shi, X. G. Liu, K. Zhou, L. Y. Wei, S. H. Teng, H. J. Bao, B. G. Guo and H. Y. Shum.

  3. Vector Field Based Shape Deformations Wolfram von Funck, Holger Theisel, Hans-Peter Seidel MPI Informatik

  4. Basic Model Moving vertex along the deformation orbit – defined by the path lines of a vector field v.

  5. Path Line of Vector Field X(t) X(t0) t0 t Given a time-dependent vector field V(X, t), a Path Line in space is X(t): OR

  6. Vector Field Selection • Deformation Request: • No self-intersection • Volume-preserving • Details-preserving • Smoothness of shape in deformation • Divergence-free Vector Field: V=(V1, V2, V3)

  7. Construction of V • Divergence-free p, q: two scalar field 2D space: 3D space:

  8. Vector Field for Special Deformation • Constant Vector Field V : translation Deformation

  9. Vector Field for Special Deformation • Linear Vector Field V : rotation Deformation

  10. Piecewise Field for Deformation • Deformation for a selected region • Define piecewise continuous field • Inner region: V • Outer region: zero • Intermediate region: blending Region specified by an implicit function And thresholds

  11. Piecewise Field for Deformation Inner region Outer region Intermediate region

  12. Piecewise Field for Deformation if if if if if if

  13. Deformation Tools • Translation: constant vector field

  14. Deformation Tool • Rotation: linear vector field

  15. Path Line Computation Runge-Kutta Integration For each vertex v(x,ti), integrating vector field above to v(x’, ti+1)

  16. Remeshing Edge Split

  17. Examples • Demo

  18. Examples

  19. Performance • Benchmark Test AMD 2.6GHz 2 GB RAM GeForce 6800 GT GPU

  20. Conclusion • Embeded in Vector Field • FFD • Parallel processing • Salient Strength • No self-intersection • Volume-preserving • Details-preserving • Smoothness of shape in deformation

  21. A Fast Multigrid Algorithm for Mesh Deformation Lin Shi, Yizhou Yu, Nathan Bell, Wei-Wen Feng University of Illinois at Urbana-Champaign

  22. Basic Model • Two-pass pipeline • Local Frame Update • Vertex Position Update • Multigrid Computation Method R. Zayer, C. Rossl, Z. Karni and H. P. Seidel. Harmonic Guidance for Surface Deformation. EG2005. Y. Lipman, O. Sorkine, D. Levin and D. Cohen-Or. Linear rotation-invariant coordinates for meshes. Siggraph2005.

  23. Discrete Form (SIG’05) First Discrete Form

  24. Discrete Form (SIG’05) Second Discrete Form

  25. Local Frame (SIG’05) • Discrete Frame at each vertex forms a right-hand orthonormal basis.

  26. First Pass (EG’05) • Harmonic guidance for local frame Boundary conditions: 1: edited vertex 0: fixed vertex 1 0 • Scaling • Rotation

  27. Second Pass (SIG’05) • Solving vertex position

  28. Second Pass • Solving vertex position “Normal Equation”

  29. Some Results

  30. Computation • First Pass • Second Pass Multigrid Method

  31. Multigrid Method defect equation coarsest level

  32. Performance

  33. Performance

  34. Conclusion • Computation Method for large mesh

  35. Editing Arbitrary Deforming Surface Animations S. Kircher, M. Garland University of Illinois at Urbana-Champaign

  36. Problem Deforming Surface Editing Surface

  37. Pyramid Scheme • Quadric Error Metric M. Garland and P. S. Heckbert. Surface simplification using quadric error metrics. SIGGRAPH’97.

  38. Pyramid Scheme Detail vector Coarse Fine 2nd-order divided difference Sig’99 Construct by and adding detail vectors for level k.

  39. Adaptive Transform

  40. Adaptive Transform • Multilevel Meshes (Sig’05) Reclustering is generated from by improving its error with respect to Swap

  41. Basis Smoothing • Blockification • Vertex Teleportation PRE-processing: Time-varying multiresolution transform for a given animation sequence.

  42. Editing Tool • Direct Manipulation level 0 level k

  43. Editing Tool • Direct Manipulation

  44. Editing Tool • Direct Manipulation

  45. Multiresolution Embossing Multiresolution set of Edit

  46. Conclusion • Multiresolution Edit

  47. The End